/*
 * jidctint.c
 *
 * Copyright (C) 1991-1994, Thomas G. Lane.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README file.
 *
 * This file contains a slow-but-accurate integer implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
 * on each row (or vice versa, but it's more convenient to emit a row at
 * a time).  Direct algorithms are also available, but they are much more
 * complex and seem not to be any faster when reduced to code.
 *
 * This implementation is based on an algorithm described in
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
 * The primary algorithm described there uses 11 multiplies and 29 adds.
 * We use their alternate method with 12 multiplies and 32 adds.
 * The advantage of this method is that no data path contains more than one
 * multiplication; this allows a very simple and accurate implementation in
 * scaled fixed-point arithmetic, with a minimal number of shifts.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"        /* Private declarations for DCT subsystem */

#ifdef DCT_ISLOW_SUPPORTED


/*
 * This module is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
Sorry, this code only copes with 8 x8 DCTs.  /* deliberate syntax err */
    #endif


/*
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
 * larger than the true IDCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D IDCT,
 * because the y0 and y4 inputs need not be divided by sqrt(N).
 *
 * We have to do addition and subtraction of the integer inputs, which
 * is no problem, and multiplication by fractional constants, which is
 * a problem to do in integer arithmetic.  We multiply all the constants
 * by CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (To scale up 12-bit sample data further, an
 * intermediate INT32 array would be needed.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#define PASS1_BITS  1       /* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 13
#define FIX_0_298631336  ( (INT32)  2446 )    /* FIX(0.298631336) */
#define FIX_0_390180644  ( (INT32)  3196 )    /* FIX(0.390180644) */
#define FIX_0_541196100  ( (INT32)  4433 )    /* FIX(0.541196100) */
#define FIX_0_765366865  ( (INT32)  6270 )    /* FIX(0.765366865) */
#define FIX_0_899976223  ( (INT32)  7373 )    /* FIX(0.899976223) */
#define FIX_1_175875602  ( (INT32)  9633 )    /* FIX(1.175875602) */
#define FIX_1_501321110  ( (INT32)  12299 )   /* FIX(1.501321110) */
#define FIX_1_847759065  ( (INT32)  15137 )   /* FIX(1.847759065) */
#define FIX_1_961570560  ( (INT32)  16069 )   /* FIX(1.961570560) */
#define FIX_2_053119869  ( (INT32)  16819 )   /* FIX(2.053119869) */
#define FIX_2_562915447  ( (INT32)  20995 )   /* FIX(2.562915447) */
#define FIX_3_072711026  ( (INT32)  25172 )   /* FIX(3.072711026) */
#else
#define FIX_0_298631336  FIX( 0.298631336 )
#define FIX_0_390180644  FIX( 0.390180644 )
#define FIX_0_541196100  FIX( 0.541196100 )
#define FIX_0_765366865  FIX( 0.765366865 )
#define FIX_0_899976223  FIX( 0.899976223 )
#define FIX_1_175875602  FIX( 1.175875602 )
#define FIX_1_501321110  FIX( 1.501321110 )
#define FIX_1_847759065  FIX( 1.847759065 )
#define FIX_1_961570560  FIX( 1.961570560 )
#define FIX_2_053119869  FIX( 2.053119869 )
#define FIX_2_562915447  FIX( 2.562915447 )
#define FIX_3_072711026  FIX( 3.072711026 )
#endif


/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 * For 12-bit samples, a full 32-bit multiplication will be needed.
 */

#if BITS_IN_JSAMPLE == 8
#define MULTIPLY( var, const )  MULTIPLY16C16( var, const )
#else
#define MULTIPLY( var, const )  ( ( var ) * ( const ) )
#endif


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce an int result.  In this module, both inputs and result
 * are 16 bits or less, so either int or short multiply will work.
 */

#define DEQUANTIZE( coef, quantval )  ( ( (ISLOW_MULT_TYPE) ( coef ) ) * ( quantval ) )


/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */

GLOBAL void
jpeg_idct_islow( j_decompress_ptr cinfo, jpeg_component_info * compptr,
                 JCOEFPTR coef_block,
                 JSAMPARRAY output_buf, JDIMENSION output_col ) {
    INT32 tmp0, tmp1, tmp2, tmp3;
    INT32 tmp10, tmp11, tmp12, tmp13;
    INT32 z1, z2, z3, z4, z5;
    JCOEFPTR inptr;
    ISLOW_MULT_TYPE * quantptr;
    int * wsptr;
    JSAMPROW outptr;
    JSAMPLE * range_limit = IDCT_range_limit( cinfo );
    int ctr;
    int workspace[DCTSIZE2];/* buffers data between passes */
    SHIFT_TEMPS

    /* Pass 1: process columns from input, store into work array. */
    /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
    /* furthermore, we scale the results by 2**PASS1_BITS. */

    inptr = coef_block;
    quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
    wsptr = workspace;
    for ( ctr = DCTSIZE; ctr > 0; ctr-- ) {
        /* Due to quantization, we will usually find that many of the input
         * coefficients are zero, especially the AC terms.  We can exploit this
         * by short-circuiting the IDCT calculation for any column in which all
         * the AC terms are zero.  In that case each output is equal to the
         * DC coefficient (with scale factor as needed).
         * With typical images and quantization tables, half or more of the
         * column DCT calculations can be simplified this way.
         */

        if ( ( inptr[DCTSIZE * 1] | inptr[DCTSIZE * 2] | inptr[DCTSIZE * 3] |
               inptr[DCTSIZE * 4] | inptr[DCTSIZE * 5] | inptr[DCTSIZE * 6] |
               inptr[DCTSIZE * 7] ) == 0 ) {
            /* AC terms all zero */
            int dcval = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] ) << PASS1_BITS;

            wsptr[DCTSIZE * 0] = dcval;
            wsptr[DCTSIZE * 1] = dcval;
            wsptr[DCTSIZE * 2] = dcval;
            wsptr[DCTSIZE * 3] = dcval;
            wsptr[DCTSIZE * 4] = dcval;
            wsptr[DCTSIZE * 5] = dcval;
            wsptr[DCTSIZE * 6] = dcval;
            wsptr[DCTSIZE * 7] = dcval;

            inptr++;    /* advance pointers to next column */
            quantptr++;
            wsptr++;
            continue;
        }

        /* Even part: reverse the even part of the forward DCT. */
        /* The rotator is sqrt(2)*c(-6). */

        z2 = DEQUANTIZE( inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] );
        z3 = DEQUANTIZE( inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] );

        z1 = MULTIPLY( z2 + z3, FIX_0_541196100 );
        tmp2 = z1 + MULTIPLY( z3, -FIX_1_847759065 );
        tmp3 = z1 + MULTIPLY( z2, FIX_0_765366865 );

        z2 = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] );
        z3 = DEQUANTIZE( inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] );

        tmp0 = ( z2 + z3 ) << CONST_BITS;
        tmp1 = ( z2 - z3 ) << CONST_BITS;

        tmp10 = tmp0 + tmp3;
        tmp13 = tmp0 - tmp3;
        tmp11 = tmp1 + tmp2;
        tmp12 = tmp1 - tmp2;

        /* Odd part per figure 8; the matrix is unitary and hence its
         * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
         */

        tmp0 = DEQUANTIZE( inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] );
        tmp1 = DEQUANTIZE( inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] );
        tmp2 = DEQUANTIZE( inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] );
        tmp3 = DEQUANTIZE( inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] );

        z1 = tmp0 + tmp3;
        z2 = tmp1 + tmp2;
        z3 = tmp0 + tmp2;
        z4 = tmp1 + tmp3;
        z5 = MULTIPLY( z3 + z4, FIX_1_175875602 );/* sqrt(2) * c3 */

        tmp0 = MULTIPLY( tmp0, FIX_0_298631336 );/* sqrt(2) * (-c1+c3+c5-c7) */
        tmp1 = MULTIPLY( tmp1, FIX_2_053119869 );/* sqrt(2) * ( c1+c3-c5+c7) */
        tmp2 = MULTIPLY( tmp2, FIX_3_072711026 );/* sqrt(2) * ( c1+c3+c5-c7) */
        tmp3 = MULTIPLY( tmp3, FIX_1_501321110 );/* sqrt(2) * ( c1+c3-c5-c7) */
        z1 = MULTIPLY( z1, -FIX_0_899976223 );/* sqrt(2) * (c7-c3) */
        z2 = MULTIPLY( z2, -FIX_2_562915447 );/* sqrt(2) * (-c1-c3) */
        z3 = MULTIPLY( z3, -FIX_1_961570560 );/* sqrt(2) * (-c3-c5) */
        z4 = MULTIPLY( z4, -FIX_0_390180644 );/* sqrt(2) * (c5-c3) */

        z3 += z5;
        z4 += z5;

        tmp0 += z1 + z3;
        tmp1 += z2 + z4;
        tmp2 += z2 + z3;
        tmp3 += z1 + z4;

        /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

        wsptr[DCTSIZE * 0] = (int) DESCALE( tmp10 + tmp3, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 7] = (int) DESCALE( tmp10 - tmp3, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 1] = (int) DESCALE( tmp11 + tmp2, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 6] = (int) DESCALE( tmp11 - tmp2, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 2] = (int) DESCALE( tmp12 + tmp1, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 5] = (int) DESCALE( tmp12 - tmp1, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 3] = (int) DESCALE( tmp13 + tmp0, CONST_BITS - PASS1_BITS );
        wsptr[DCTSIZE * 4] = (int) DESCALE( tmp13 - tmp0, CONST_BITS - PASS1_BITS );

        inptr++;        /* advance pointers to next column */
        quantptr++;
        wsptr++;
    }

    /* Pass 2: process rows from work array, store into output array. */
    /* Note that we must descale the results by a factor of 8 == 2**3, */
    /* and also undo the PASS1_BITS scaling. */

    wsptr = workspace;
    for ( ctr = 0; ctr < DCTSIZE; ctr++ ) {
        outptr = output_buf[ctr] + output_col;
        /* Rows of zeroes can be exploited in the same way as we did with columns.
         * However, the column calculation has created many nonzero AC terms, so
         * the simplification applies less often (typically 5% to 10% of the time).
         * On machines with very fast multiplication, it's possible that the
         * test takes more time than it's worth.  In that case this section
         * may be commented out.
         */

#ifndef NO_ZERO_ROW_TEST
        if ( ( wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] |
               wsptr[7] ) == 0 ) {
            /* AC terms all zero */
            JSAMPLE dcval = range_limit[(int) DESCALE( (INT32) wsptr[0], PASS1_BITS + 3 )
                                        & RANGE_MASK];

            outptr[0] = dcval;
            outptr[1] = dcval;
            outptr[2] = dcval;
            outptr[3] = dcval;
            outptr[4] = dcval;
            outptr[5] = dcval;
            outptr[6] = dcval;
            outptr[7] = dcval;

            wsptr += DCTSIZE;/* advance pointer to next row */
            continue;
        }
#endif

        /* Even part: reverse the even part of the forward DCT. */
        /* The rotator is sqrt(2)*c(-6). */

        z2 = (INT32) wsptr[2];
        z3 = (INT32) wsptr[6];

        z1 = MULTIPLY( z2 + z3, FIX_0_541196100 );
        tmp2 = z1 + MULTIPLY( z3, -FIX_1_847759065 );
        tmp3 = z1 + MULTIPLY( z2, FIX_0_765366865 );

        tmp0 = ( (INT32) wsptr[0] + (INT32) wsptr[4] ) << CONST_BITS;
        tmp1 = ( (INT32) wsptr[0] - (INT32) wsptr[4] ) << CONST_BITS;

        tmp10 = tmp0 + tmp3;
        tmp13 = tmp0 - tmp3;
        tmp11 = tmp1 + tmp2;
        tmp12 = tmp1 - tmp2;

        /* Odd part per figure 8; the matrix is unitary and hence its
         * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
         */

        tmp0 = (INT32) wsptr[7];
        tmp1 = (INT32) wsptr[5];
        tmp2 = (INT32) wsptr[3];
        tmp3 = (INT32) wsptr[1];

        z1 = tmp0 + tmp3;
        z2 = tmp1 + tmp2;
        z3 = tmp0 + tmp2;
        z4 = tmp1 + tmp3;
        z5 = MULTIPLY( z3 + z4, FIX_1_175875602 );/* sqrt(2) * c3 */

        tmp0 = MULTIPLY( tmp0, FIX_0_298631336 );/* sqrt(2) * (-c1+c3+c5-c7) */
        tmp1 = MULTIPLY( tmp1, FIX_2_053119869 );/* sqrt(2) * ( c1+c3-c5+c7) */
        tmp2 = MULTIPLY( tmp2, FIX_3_072711026 );/* sqrt(2) * ( c1+c3+c5-c7) */
        tmp3 = MULTIPLY( tmp3, FIX_1_501321110 );/* sqrt(2) * ( c1+c3-c5-c7) */
        z1 = MULTIPLY( z1, -FIX_0_899976223 );/* sqrt(2) * (c7-c3) */
        z2 = MULTIPLY( z2, -FIX_2_562915447 );/* sqrt(2) * (-c1-c3) */
        z3 = MULTIPLY( z3, -FIX_1_961570560 );/* sqrt(2) * (-c3-c5) */
        z4 = MULTIPLY( z4, -FIX_0_390180644 );/* sqrt(2) * (c5-c3) */

        z3 += z5;
        z4 += z5;

        tmp0 += z1 + z3;
        tmp1 += z2 + z4;
        tmp2 += z2 + z3;
        tmp3 += z1 + z4;

        /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

        outptr[0] = range_limit[(int) DESCALE( tmp10 + tmp3,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[7] = range_limit[(int) DESCALE( tmp10 - tmp3,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[1] = range_limit[(int) DESCALE( tmp11 + tmp2,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[6] = range_limit[(int) DESCALE( tmp11 - tmp2,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[2] = range_limit[(int) DESCALE( tmp12 + tmp1,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[5] = range_limit[(int) DESCALE( tmp12 - tmp1,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[3] = range_limit[(int) DESCALE( tmp13 + tmp0,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[4] = range_limit[(int) DESCALE( tmp13 - tmp0,
                                               CONST_BITS + PASS1_BITS + 3 )
                                & RANGE_MASK];

        wsptr += DCTSIZE;   /* advance pointer to next row */
    }
}

#endif /* DCT_ISLOW_SUPPORTED */
